1. Field of the Invention
The present invention is an improved apparatus for measuring the interfacial tension between two liquids having different densities.
When two immiscible liquids are in contact, the work required by the molecules to reduce their respective surface areas is conventionally known as interfacial tension. Interfacial forces govern such phenomena as the wetting or nonwetting of solids by liquids and the capillary rise of liquids in fine tubes and wicks. The measurement of interfacial tension is important to several technologies and industrial applications, including detergents, anti-frothing agents and soaps.
2. Description of the Prior Art.
An instrument for measuring interfacial tension between two fluids is disclosed in U.S. Pat. No. 4,250,741 issued to Scriven, II et al. The Scriven instrument is based upon the spinning drop technique, one of the conventional shape methods of the known art for measuring fluid interfacial tension. The Scriven instrument includes a sample tube for containing the fluids and a hosuing for enclosing the tube. A massive bearing housing contains a precision ground shaft and is connected to the sample tube. The shaft is rotated by a motor causing the tube to rotate at the same rate.
To measure interfacial tension between two fluids with the Scriven device, a single drop of the less dense fluid is loaded into a tube filled with the more dense fluid. The tube is spun until gyrostatic equilibrium is reached and the drop migrates to an ever-so-slightly elevated end of the tube for viewing. Typically, a drop takes four to six hours to migrate to the desired position. In some cases, the drop may be kept spinning for days. Compressed air is forced into the bearing housing to maintain temperatures during operation of the instrument. When all required conditions are met, the apparent drop diameter is measured by a microscope and the rotational speed of the drop is recorded.
The Scriven device has several drawbacks. First, the Scriven tensiometer requires specially constructed equipment and parts. Second, interfacial tension measurements can require a great deal of time and skill. Third, loading the fluids in the sample tube can be difficult, particularly when attempting to keep the drop of lighter fluid away from the sides of the tube. Further, if the drop assumes an oblong shape at the time the diameter is measured, inaccurate results may result.
The theory for the present device was developed in an article by Joseph et al (D.D. Joseph, Y. Renardy, M. Renardy and K. Hguyen, 153 J. Fluid Mech. 151 (1985)). The article considered the flow of two immiscible liquids of different viscosities and densities rotated between concentric cylinders. The interface between the two fluids has a constant radius when the density difference, represented by [.rho.], is positive, and when the more dense fluid is centrifuged to the outer portions of the outer cylinder. The relationship between interfacial tension T and the radius of the interface r is expressed as: EQU ([.rho.]r.sup.3 .OMEGA..sup.2)/T.gtoreq.4 (1)
where, .OMEGA. is the angular velocity of the cylinders around the axis of symmetry.
The inequality (1) does not hold for free drops. When .OMEGA. is large, the free drop is cigar shaped, and a constant d appears only in an approximate sense. As .OMEGA. is increased the drop will elongate and its radius (r) will decrease in such a way that EQU ([.rho.]r.sup.3 .OMEGA..sup.2)/T=4 (2)
approximately. Equation (2) is the basis of both the spinning drop and the spinning rod tensiometer. If the drop is kept from elongating, say by blocking the elongation with end plates perpendicular to the axis of rotation, then a constant radius can be achieved. Further increases of .OMEGA. do not change the shape of the interface and the inequality (1) is appropriate.